To simplify notations let us assume there are two currencies: dollars ($) for domestic country and euros () for foreign country. Annual interest rate for deposits in dollars in the domestic country is R$ and annual interest rate for deposits in euros in the foreign country is R. Todays spot exchange rate of dollars for euros (i.e., how many dollars you pay to buy one euro) is E$/. The forward rate over one year is F$/.

Now suppose further that anytime you would exchange dollars for euros or euros for dollars there is a commission you have to pay calculated as a fraction ? of the amount in dollars exchanged. To clarify: say you want to exchange $100 into euros at an exchange rate E$/: a fraction ? of the $100 is paid as commission and remaining $100?(1 ?) is exchanged into $100?(1 ?)/E$/ euros. Conversely, say you would want to exchange 100 into dollars at an exchange rate E$/: the initial 100 will result in 100? E$/ dollars of which a fraction ? is paid as commission with a remaining amount of 100?E$/?(1 ?) dollars.

Part i. [8 points] You start with $1 in hand and contemplate two strategies:

(A) invest in the domestic country in dollars for one year, and

(B) exchange the $1 into euros today at the exchange rate E$/,

enter a one year forward contract at F$/, invest the available euros in the foreign country for a year, and at the end of the year exchange the resulting euros back into dollars.

Write down the condition that guarantees that you will prefer to adopt Strategy A rather than Strategy B. Part ii. [8 points] You start with 1 in hand and contemplate two strategies:

(C) invest in the foreign country in euros for one year, and (D) exchange the 1 into dollars today at the exchange rate E$/,

enter a one year forward contract at F$/, invest the available dollars in the domestic country for a year, and at the end of the year exchange the resulting dollars back into euros.

Write down the condition that guarantees that you will prefer to adopt Strategy C rather than Strategy D.

Part iii. [4 points] Combine the conditions from Part i and Part ii above to derive a covered interest parity condition with omission. Verify that setting ? = 0 in this condition will give you immediately the CIP as derived in class. Hint: you should obtain something of the form (1 + R)?... ? 1 + R$ ? (1 + R)?....